Question

State the units for intensity using only fundamental units?

Answer 1

In order to solve this question, we should know that the units of physical quantities which can’t derived from any other physical quantities are known as fundamental units, so here we will first know about these seven fundamental units in physics and then we will derive the unit of intensity in terms of fundamental units.

Complete step by step solution:
In physics, there are only seven fundamental units and these are mentioned below along with their units and symbols used for notations.

Fundamental physical Quantity	Unit	Symbol
Length	meter	m
Time	seconds	s
Temperature	Kelvin	K
Amount of substance	mole	mol
Electric current	Ampere	A
Luminous Intensity	Candela	cd
Mass	Kilogram	kg

Now, coming to the question we need to find units of Intensity with using the relation of $\dfrac{W}{{{m^2}}}$
Intensity is defined as the power acting on the surface of a body per unit of area as $I = \dfrac{P}{A}$ where I, P, A denote intensity, Power, area.
We know that, SI unit of power can be written as $P = F \times v$ where F is force and v is velocity so, units of force in terms of fundamental units is $kgm{s^{ - 2}}$ and units of velocity is $m{s^{ - 1}}$
hence, units of power Watt can be written as $W = kgm{s^{ - 2}} \times m{s^{ - 1}}$
$W = kg{m^2}{s^{ - 3}}$
Now, SI unit of area is simply ${m^2}$ so, SI unit of Intensity can be written as
$I = \dfrac{P}{A} = \dfrac{W}{{{m^2}}}$ on putting the value of watts (W) we get,
$I = \dfrac{{kg{m^2}{s^{ - 3}}}}{{{m^2}}}$
$I = kg{s^{ - 3}}$
Hence, SI units of intensity in terms of fundamental units is $kg{s^{ - 3}}$.

Note:
It should be remembered that, any physical quantity other than these seven fundamental quantities can be written in terms of seven fundamental units and units of such physical quantities are called derived units so, whenever asked to write units of any quantity in terms of fundamental units always derive the formula of asked quantity in terms of fundamental quantities.